In this paper, we consider the subset selection problem for function f with constraint bound B which changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a φ = (α f /2)(1 − 1 e α f )-approximation, where α f is the submodularity ratio of f , for each possible constraint bound b ≤ B. Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that B increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. In this paper, we study singleand multi-objective baseline evolutionary algorithms for the classical knapsack problem where the capacity of the knapsack varies over time.We establish different benchmark scenarios where the capacity changes every τ iterations according to a uniform or normal distribution. Our experimental investigations analyze the behavior of our algorithms in terms of the magnitude of changes determined by parameters of the chosen distribution, the frequency determined by τ and the class of knapsack instance under consideration. Our results show that the multi-objective approaches using a population that caters for dynamic changes have a clear advantage on many benchmarks scenarios when the frequency of changes is not too high.
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